More About Crop Circles

The following exchange about an article previously published in the Journal ofScientific Exploration exceeds in length our guidelines for letters, and to someextent our guidelines as to precise focus on specific points. However, we feltobliged to allow Haselhoff to have his say after our publication of a piece thathad criticized some of his writings.

That earlier piece we had published, as noted at the time, because the journalthat had disseminated the work being commented on had refused to accept thiscommentary—in retrospect, it regretted having given any space at all to the matterof crop circles. The Journal of Scientific Exploration, of course, is open preciselyto topics excluded from venues of orthodoxy, and we also believe that a journalthat has published something should permit at least one dissenting critique.

However, we will call a halt at this stage to the present to-and-fro. Any futuresubmissions on the question of crop circles will need to be full manuscripts, andwill be reviewed under our customary stringency as to focus, presentedevidence, statistical inference, and logical discussion.

HENRY H. BAUER

hhbauer@pop.vt.edu

Haselhoff Responds to ‘‘Balls of Light: The QuestionableScience of Crop Circles’’

I would like to comment on a paper in your Journal (Grassi, Cocheo, & Russo,2005) that criticizes three other papers, two of which were written by the BLTResearch Group (Levengood 1994; Levengood & Talbott, 1999) and one waswritten by myself (Haselhoff, 2001). The analysis by Grassi et al. containsseveral serious mistakes, which renders most of their conclusions invalid.

First, Grassi et al. criticize the simplicity and question the physical validity ofthe balls of light (BOL) model as suggested in my comment (Haselhoff, 2001).They require explicit inclusion of mechanisms such as cumulative energyabsorption, effects of moisture, reflection, spectral distribution, and the incidentangle of the alleged radiation source. Although these suggestions are validrecommendations for future research, I believe they cannot be taken seriously as

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a point of criticism of my comment, which was merely suggesting a modificationof the interpretations by the BLT Research Group. The modified interpretationmatches an apparently genuine physical counterpart, namely, the ‘‘balls of light’’that have been witnessed and filmed in and around several crop formations.Moreover, the suggestions for extension of the BOL model made by Grassi et al.are not realistic because the results published by BLT (Levengood & Talbott,1999) are not based on laboratory experiments, performed in a controlledenvironment, but on an analysis of circumstantial evidence, in the form of anapparent leftover of a largely unknown process. With the currently availabledata, the implementation of an advanced physical model like Grassi et al.suggest will only raise more questions than it could ever answer.

Next, Grassi et al. (2005: p. 163) go into some depth with respect to what theycall a ‘‘questionable sampling strategy’’. It is unfortunate that they neglect tomake a clear distinction between the fieldwork performed by BLT versus theadditional verifications by myself (carried out using the same field protocols).The concerns that Grassi et al. raise with respect to the choice of controls, theinclusion or exclusion of standing stems in the analyses, etc., are all results ofa profound misunderstanding of the work by BLT. Grassi et al. (2005: p. 165)demonstrate this at several points in their paper, e.g., when they state that ‘‘Nostatistical tests have been performed to compare means and variances’’, whilethis is a standard procedure for all work carried out by BLT. Moreover, it wasalso clearly stated by BLT in their papers that standard t-tests were performed,and that all results obeyed the common p , 0.05 criteria. Grassi et al. (2005:p. 166) demonstrate their poor understanding of these matters in their Tables 2aand 2b. These tables are used to question the statistical validity and the physicalmeaning of the BOL model, based on a calculation of p-values. First of all, thep-values published in Table 2a for the height parameter h are not the values forh, but for h2. It is easy to understand that the p-values for h2 are considerablyhigher. Much worse, however, is that all p-values published by Grassi et al.correspond to the case of single node length measurements, i.e., the measurementof single nodes at various positions in the field (N¼ 1). This, of course, was notthe case, and Grassi et al. even report themselves that all node lengths used inthe analysis by BLT were average values of 15–20 nodes for each position in thefield, whereas—as explicitly reported by BLT in their papers—all variations innode length were in fact statistically significant. The fact that Grassi et al.clearly failed to recognize this, renders their entire statistical analysis invalid,along with most of the conclusions in their paper.

The crux of the work presented by BLT was the discovery that node lengths ina field with crop formations sometimes show statistically significant (p , 0.05)variations, geometrically correlated to the imprints in the fields, both in flattenedand in standing crop. This remains an interesting finding, which I still believerequires further study. However, this essential fact was clearly not understood byGrassi et al.

Also some remarks must be made with regard to the analysis by Grassi et al.

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of the Nieuwerkerk formation. Their findings are exclusively based on raw data,which I sent to them at their request. The spreadsheet only contained rawnumbers with a minimum of explanations, but despite the fact that we latercommunicated several times, Grassi et al. never discussed the interpretation ofmy data with me until after the press release announcing their publication. Asa result, some unfortunate mistakes have been made. For example, the positionsof the control samples that Grassi et al. assumed, and used in their analysis, wereall wrong. A more relevant point of concern is related to the alternative outcomefor the correlation coefficient, as presented by Grassi et al., by using the averagevalues of corresponding samples in two different radial sample sets. This is notallowed because such an approach would require the explicit assumption ofcircular symmetry of the node length distribution in the crop circle. Obviously,such an assumption cannot be made a priori because this is exactly the issue thatthe BOL analysis should investigate. Subsequently, the authors also include thesamples outside the flattened area in their analysis despite the fact that these hadalready been used for the determination of the control value (Grassi, 2006). Inthis way they manage to increase the correlation coefficient to R2¼ 0.699, andthey conclude that the man-made formation reveals characteristics ofa ‘‘genuine’’ crop circle. However, the inclusion of the extra data does not atall demonstrate a better fit to the BOL model despite the (moderate) increase ofthe correlation coefficient. This can be seen in Figure 1, where the data pointsadded by Grassi et al. are shown as open dots. Two of the added data points evenrepresent a shrinkage of the node length (the node length increase is negative),violating the assumptions of the BOL model. Apparently, the correlationcoefficient alone is not an adequate indicator. The reasoning of Grassi et al. inthis matter is flawed and has no physical counterpart, so that their conclusion isinvalid. In order to reach solid conclusions in this matter, more statistical data onman-made formations is needed by performing new, original research. This isthe basis of an ongoing study carried out by myself and others, to be publishedlater this year.

Summarizing, Grassi et al. conclude that the findings presented by BLT(Levengood 1994; Levengood and Talbott, 1999) demonstrate nothing buta difference in node elongation between flattened and upright plants, whichcould be the result of whatever flattening mechanism. Their conclusion is in linewith their erroneous statistical analysis, for which each data pair is incorrectlyinterpreted as the result of a single stem measurement. In reality, however, allreported variances in node length were statistically significant, with a clearcorrelation to the geometrical imprints in the field, i.e., depending on the lineardistance from the imprints. The fact that this crucial aspect of the two BLTpapers was not recognized by Grassi et al. renders most of their statementsinvalid.

Despite the fact that I would have preferred a more open and particularlya more honest communication, I would like to thank Mr. Grassi and his

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co-authors for their interest in our work. Their recommendations will beconsidered for future research.

ELTJO H. HASELHOFF

EltjoHaselhoff@planet.nl

References

Grassi, F. (2006). Personal communication.

Grassi, F., Cocheo, C., & Russo, P. (2005). Balls of light: the questionable science of crop circles.Journal of Scientific Exploration, 19(2), 159–170.

Haselhoff, E. H. (2001). Opinions and comments on Levengood WC, Talbott NP (1999). Phys.Plantarum, 111, 123–125.

Levengood, W. C. (1994). Anatomical Anomalies in Crop Formation Plants. Phys. Plantarum, 92,356–363.

Levengood, W. C., & Talbott, N. P. (1999). Dispersion of Energies in World Wide Crop Formations.Phys. Plantarum, 105, 615–624.

Fig. 1. Analysis of the Nieuwerkerk formation as carried out by Grassi et al. Horizontal axis:distance from circle center; vertical axis: node length increase. The open dots represent dataadded by Grassi et al. According to the authors, these improve the fit to the BOL model(indicated by the solid curve). However, the horizontal coordinates of the three rightmostopen dots are not correct, whereas two open dots correspond to node length decrease, henceviolating the BOL model.

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Grassi, Cocheo, and Russo’s Reply

Haselhoff’s remarks are welcome, but unfortunately they are not relevant, as weare going to explain.

About the BOL model complexity: to make a simple model is good, but tomake it unrealistic is not. Factors can be eliminated only after their impact hasbeen estimated as unimportant; no such assumption can be made without ananalysis. In particular, the transparency of the tissue to the radiation looks likea relevant factor that should not be eliminated without justification: a perfectlytransparent tissue would not be affected at all, while a non-transparent stemwould partially shield its nodes from radiation, depending on the incidenceangle. The correctness of a model is independent of whether the environment iscontrolled or not. It is obvious that a more complex model may require moredata to be validated, but this can hardly justify not making a correct model.

Haselhoff1 already tried to justify some weak points of his paper on the basisthat it was a mere comment; as we explained,2 we think it is not a validjustification. The ‘‘apparently genuine’’ witness and film evidence for BOLsmentioned by Haselhoff is questionable for scientific purposes. A survey wouldbe out of place here; we just supply a few links3 to some information about theonly named witness in Haselhoff’s comment paper so that the reader can judgehow ‘‘apparently genuine’’ his claims are.

About our supposed misunderstanding of BLT’s and Haselhoff’s datahandling: although Haselhoff seems to disagree, BLT never wrote (in any oftheir scientific papers, at least) about t-tests on the data of the Devizes, Chehalis,and Sussex formations. The claims by BLT and Haselhoff that we discussedwere based only on those three formations. BLT did mention t-tests for otherdata (Beckhampton, Maryland) and that is all. Should we—or anybody—beexpected to guess about unpublished tests? However, t-tests should be addressedto compare the averages of the sample groups collected, but, as we clearly statedin our conclusions, we did not dispute the average difference between samplescollected in and out of the formation; rather, we highlighted the lack of a reliablecriterion for labelling the data as ‘‘affected’’ or ‘‘control’’.

We computed the p-value for h2, not for h, because errors propagate from thedata to h2 in the model, so h2 is the term whose significance has to be taken intoaccount. Interpreting that term as the square (or cube or nth power) of somethingelse does not change the model curve.

It is curious that Haselhoff points out that we ‘‘incorrectly’’ handled the dataas if they were single samples because that is exactly how he and BLT handledthem in their regressions; should they have taken the number and variance ofsamples into account, the resulting correlation coefficients would have beenmuch lower. Maybe the result would have been significant, but a significantmismatch. Since there may be some rationales for regressing the data in thatway, instead of raising another issue, our goal was just to evaluate the

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significance of their regressions—just as they were. However, our first remark inthis area was (and is) that both the number of circles taken into account and thenumber of samples collected in each are inadequate for a reliable statisticalanalysis; many of the specific problems we discussed are just a consequence.

Haselhoff misrepresents his and BLT’s work when he states that they justfound apparently non-random patterns deserving—in their opinion—of furtherstudy. First, the alleged t-tests mentioned by Haselhoff would not support thepresence of any pattern anyway, but only the undisputed fact that in any circle—known man-made formations included—inner plants have longer nodes thanouter ones. But even if the existence of a generic decrease-with-distance trendshould be proved, it would be a very humble and unsurprising conclusionbecause it would bear no indication of any specific cause; possible causesinclude mundane factors such as the dynamics of wind near the circle bordersand the behavior of circlemakers. On the contrary, the titles of their paperscontain words like ‘‘anomalies’’ and ‘‘energies’’ and the texts go far beyond. Wealready replied to Haselhoff’s past minimization attempts.2

About Nieuwerkerk: the position of the control samples is not so wrong.Haselhoff4 sent us a file listing the sample values and distances from the centerof a circle; he only recently informed us that the control samples were taken atthe listed distances, but from another circle in the same formation.4 However,those two circles were identical under all respects due to the symmetry of theformation, and there is no reason to suppose different creation mechanisms, andthus we fail to appreciate the relevance of Haselhoff’s comment. Anyway, evenaccepting that supposition and using the corrected distance from the correctedcircle, the correlation coefficient does not change significantly. About Hasel-hoff’s other comments on the same circle: he would be correct if we everclaimed that the Nieuwerkerk circle (a known man-made formation) hadactually been created by a BOL. Of course, we never did; our purpose wasentirely different. BLT’s and Haselhoff’s conclusions were based on just threecrop circles, each one sampled in just a few points with no bidimensionalinformation. Moreover, the classification of samples as ‘‘affected’’ or ‘‘control’’looked arbitrary and decided after the values were known; no comparison withalternative and possibly better fitting or physically more founded models wastried. Isn’t this procedure questionable? Can’t it lead to spurious positive-lookingresults? Not only did we explain the reasons, but we added an example. Weconsidered the known man-made Nieuwerkerk circle, which Haselhoff sampledand used as an example of a negative result, and we handled it in the same waythe other circles had been. We averaged two data sets, taken along differentradii, both to eliminate the bidimensional information (anyway, as a consequenceof the BOL spherical symmetry, no changes have to be expected by varying thedirection of the radius, the only variation depending on the distance from thecenter) and to reduce the number of samples (to seven), so that no moreinformation was available about that circle than it was for the other ones, inorder to allow for a fair comparison. Then we aggregated the data as affected/

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control in various sensible ways, showing how the resulting correlationcoefficient was affected by an arbitrary choice of each of them; the waymentioned by Haselhoff was just the last one. We do agree that the positive-looking result we obtained with a few arbitrarily aggregated data should not betaken seriously, but that exactly proves our point that Haselhoff seems to miss.He misses it even more when he proposes that if any sample value is less thanthe control level (an apparent ‘‘shrinking’’), then the model should be rejected.He cannot really think that nodes near man-made circles do shrink; that is justdata variability and is already adequately handled by statistical tests. Nonethe-less, we would accept Haselhoff’s rule if only it had been stated in advance;adjusting criteria after looking at the results is exactly one of the questionablepractices we criticized.

Finally, about the Nieuwerkerk circle, Haselhoff concludes with theadmission that ‘‘apparently, the correlation coefficient alone is not an adequateindicator’’. This is exactly our criticism of his work. We agree with him: acorrelation coefficient alone is not an adequate indicator. But that is the onlyindicator used by Haselhoff himself to try to demonstrate the existence ofa BOL. So, Haselhoff himself is admitting that the whole corpus of his work issupported only by an indicator whose adequacy is questionable.

We would also like to point out that Haselhoff’s reply does not address severalpoints we made, for example, the incoherence of the proposed physicalmechanism (thermal dilation of water) and the exclusion of several data from theanalysis (central tufts, Beckhampton circle).

In conclusion, Haselhoff’s remarks are welcome, but they do not contribute tomake his paper more reliable, nor to invalidate our criticisms of it.

FRANCESCO GRASSI

grassi@cicap.orgCLAUDIO COCHEO

PAOLO RUSSO

References

1. http://www.cicap.org/crops/en/011.htm. Accessed 26 July 2007.2. http://www.cicap.org/crops/en/012.htm. Accessed 26 July 2007.3. http://www.cicap.org/crops/en/cache/001.htm#i1. Accessed 26 July 2007.

http://www.cicap.org/crops/en/cache/002.htm#i6. Accessed 26 July 2007.http://www.cicap.org/crops/en/cache/003.htm. Accessed 26 July 2007.http://www.cicap.org/crops/en/cache/004.htm (for witness identity verification). Accessed 26 July2007.

4. Haselhoff, E. H. (2001). Personal communication.

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